consider the function f(x)4x^2 -2x-1 find the x intercepts
To find the x-intercepts of a function, you need to set f(x) equal to zero and solve for x. In this case, the function is f(x) = 4x^2 - 2x - 1.
So, setting f(x) equal to zero gives us the equation 4x^2 - 2x - 1 = 0.
To solve this quadratic equation, you can either factor it or use the quadratic formula. Let's go ahead and use the quadratic formula.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 4, b = -2, and c = -1. Plugging these values into the formula, we get:
x = (-(-2) ± √((-2)^2 - 4*4*(-1))) / (2*4)
= (2 ± √(4 + 16)) / 8
= (2 ± √20) / 8
Simplifying the expression further, we get:
x = (2 ± 2√5) / 8
This can be further simplified by dividing both the numerator and denominator by 2:
x = (1 ± √5) / 4
Therefore, the x-intercepts of the function f(x) = 4x^2 - 2x - 1 are x = (1 + √5) / 4 and x = (1 - √5) / 4.